The Federal Geodetic Control Committee (FGCC), chartered
in 1968, assists and advises the Federal Coordinator for Geodetic Control and
Related Surveys. The Federal
Coordinator for Geodetic Control is Responsible for Coordinating, planning, and
executing national geodetic control surveys and related survey activities of
Federal agencies.

The Methodology Subcommittee of FGCC is responsible for
revising and updating the Standards and Specifications for Geodetic Control
Networks.

Suppose the value m quantifies one of the components of the relative position between two marks, which may be, for example, relative height or the east-west base line component. Then the term “relative accuracy” for m will be defined as the ratio, e/d, where the interval m- to m+ corresponds to the 95% confidence region for m while d equals the distance between two marks and e equals
the component error.

For a network of stations surveyed by GPS relative positioning techniques the three components of the relative position can be determined. The term “relative position accuracy” denotes the relative accuracy of the various components for a representative pair of network marks. Consequently, a GPS network is said to have a relative positioning accuracy of 1 ppm (1:1 000 000) when each component of a representative base line has a relative accuracy of at least 1 ppm. The concept of relative position accuracy can be applied to networks where relative positions have been determined either by single-dimensional measurement or by three-dimensional space-based measurements (R. Snay, NGS, 1986 personal communications).

Accuracy standards for geometric relative positioning are based on the assumption that errors can be assumed to follow a normal distribution. Normal distribution applies only to independent random errors, assuming that systematic errors and blunders have been eliminated or reduced sufficiently to permit treatment as random errors. Although, truly normal error distribution seldom occurs in a sample of observations, it is desirable to assume a normal distribution for ease of computation and understanding.

A three-dimensional error is the error in a quantity defined by three random variables. The components of a vector base line can be expressed in terms of dX, dY, and dZ. It is assumed that the spherical standard error (ss) is equal to the linear standard error for the components or ss = sx= sy = sz.

The probability level of 95 percent is consistent with the Standards and Specifications for Geodetic Control Network (FGCC 1984). One page 1-2 of this document, it is stated “ . . . a safety factor of two . . .” is “. . . incorporated in the standards and specifications.” Since those accuracy standards were based on one-dimensional errors that exist in such positional data as elevation differences and observed lengths of lines, the factor of two, a 2sx linear
accuracy standard, is a probability of confidence level of about 95 percent.

k = the repeatable setup error in (CM) for any component (horizontal and vertical) at the 95 percent confidence level

k =
0.1pd (b), where,
kmin = 0.3 CM and kmax = 10 CM

NOTE: The value for kmin is based on current estimates for expected setup errors when the antenna is set on a tripod
at a total height of less than 5 M. When the antenna is set on a mast or tower where the height is greater than 5 M, the estimated minimum value for k may be greater than 0.3 CM. On the other hand, if the antenna is mounted on a fixed or permanently installed stand, than kmin should be less than 0.1 CM.

The value for kmax is the expected largest value for the setup error; in practice, it should be much smaller than 10 CM, typically less than 1 CM.

An elevation difference accuracy is the minimum allowable error at the 95 percent confidence level.
For simplicity and ease of computations, elevation differences (dH) are
assumed to be equal to orthometric height differences.

The height differences determined from space survey systems, such as GPS satellite surveying techniques, are with respect to a reference ellipsoid. These ellipsoid (geodetic) height differences (dh) can be converted to elevation differences (dh) by the relationship:

(dh) =
(dH) - (dN)

where (dN) is the geoid height difference.

With accurate estimates for (dN) and adequate connections
by GPS relative positioning techniques to network control points tied to
National Geodetic Vertical Datum, elevations can be determine for stations with
unknown or poorly known values.

NOTE: If GPS ellipsoid height differences are being measured for the purpose of monitoring the change in height between stations, then it is not necessary to have any accurate information on the shape of the geoid. Thus, the accuracy of the height difference depends only on the accuracy of the GPS ellipsoid height differences.

The accuracy of the GPS derived elevations for points in a survey will depend on three factors:
(1) accuracy of the GPS ellipsoid height differences, (2) accuracy of
the elevations for the network control, and (3) accuracy of the geoid height
difference estimates.

In Table 10-3, elevation difference accuracy standards at the 95 percent confidence level are proposed.
The order/class correspond to the proposed geometric relative position accuracy standards. At the high orders, the error is dominated by the accuracy for the (dN) values, whereas, for the lower orders, the major source of error is in the ellipsoid height differences.

NOTE: In developing these standards, it is assumed that errors or inconsistencies in the vertical network control are negligible. Of course, this may not be true in many cases.

p = Production factor (based on historical evidence of reliability; ratio of proposed observing sessions for a project versus final number of observed sessions)

p = f/i,

where: f = final number of observing sessions required to complete the project

i = Proposed (initial) number of observing sessions scheduled for the project,

where: i = (mn)/r

FORMULAS:

s = (mn)/r + (mn)
(p-1)/r + km

where, k is a safety factor: k = 0.1 for local projects; within 100 KM
radius.

k = 0.2 for all other projects

x = estimated number of observing days for a project: x = s/d

w = estimated number of work-weeks for a project: w = x/y

v = estimated total vectors for a project: v = rs (r-1)/2

b = estimated independent vectors for a project: b = (r-1)s

EXAMPLE:

If n
= 1.75 independent
occupations per station

m
= 50 total
stations for project

y
= 5 observing
days per week

k
= 0.2 safety
factor

r
= 4 number
of GPS receivers per observing session

d
= 2.5 average
observing sessions per day

p
= 1.1 production
factor

Then s
= 22 + 3 + 10 = 35 observing sessions

x
= 14 observing days

w
= 2.8 workweeks

b
= 105 independent vectors

COMMENTS:

In the equation to compute the number of observing
sessions (s), if there were no sessions lost due to receiver malfunctions, and
no additional sessions required to cover such factors as human error and
irregular network configuration, then

s = (mn)/r

However, the second part of the equation for computing “s”
is to allow for additional sessions to offset scheduled sessions that may be
lost due to equipment breakdown.

The third part of the equation, k(m), allows for
additional sessions that may be required due to human error, irregular network
configuration, etc.

a.The time required to set an average mark using the
following procedures is 1 to 2 hours.

b.Using the solvent cement formulated specifically for PVC,
glue the aluminum logo cap to a 600 MM
section of 130 MM PVC pipe. This will allow the glue to set while
continuing with the following setting procedures.

c.Glue the PVC cap with a drill hole on one end of a 900
MM section of schedule 40 PVC pipe 25
MM inside diameter. Pump the PVC pipe full of grease. Thoroughly clean the pen end of the pipe
with a solvent which will remove the grease.
Then glue another cap with drill hole on the remaining open end. Set aside while continuing with the next
step.

d.Using a power auger or post hole digger, drill or dig a
hole in the ground

300 - 355 MM in
diameter and 1.0 M deep.

e.Attach a standard spiral (fluted) rod entry point to one
end of a 1.2 M section of stainless steel rod with the standard 10 MM stud.
On the opposite end screw on a short 100 - 130 MM piece of rod which will be used as the
impact point for driving the rod. Drive
this section of rod with a reciprocation driver such as Whacker model BHB 25,
Pionjar model 120, or another machine with an equivalent driving force.

f.Remove the short piece of rod used for driving and screw
in a new stud. Attach another 1.20 M
section of rod. Tighten securely. Reattach the short piece of rod and drive
the new section into the ground.

g.Repeat step 6 until the rod refuses to drive further. The top of the rod should terminate about 76
MM below the ground surface.

h.When the desired depth of the rod is reached, cut off the
top removing the tapped and threaded portion of the rod leaving the top about
76 MM below ground surface. The top of the rod then must be shaped to a
smooth rounded (hemispherical) top, using a portable grinding machine to
produce a datum point. The datum point
must then be center punched to provide a plumbing (centering) point.

NOTE: For
personnel that may not have the proper cutting or grinding equipment to produce
the datum point, the following alternative procedure should be used if
absolutely necessary. When the desired
depth of the rod is obtained (an even 1.2 M section), thoroughly clean the
thread with a solvent to remove any possible remains of grease or oil that may
have been used when the rod was tapped.
Coat the threads of the datum point with Loctite and screw the datum
point into the rod. Tighten the point
firmly with vise grips to make sure it is secure. The datum point is a stainless steel 10 MM bolt with the head precisely machined to 14
MM.

i.Insert the grease filled 900 MM section of 25 MM PVC pipe
(sleeve) over the rod. The rod and
datum point should protrude through the sleeve about 76 MM.

j.Backfill and pack with sand around the outside of the
sleeve to below ground surface. Place
the 130 MM PVC and logo cap over and around the 25 MM sleeve and rod. The
access cover on the logo cap should be flush with the ground. The datum point should be about 76 MM below
the cover of the logo cap.

k.Place concrete around the outside of the 130 MM PVC and logo cap, up to the top of the logo
cover. Trowel the concrete until a smooth neat finish is produced.

l.Continue to backfill and pack with sand inside the 130 MM
PVC and around the outside of the 25 MM sleeve and rod to about 25 MM below the
top of the sleeve.

m.Remove all debris and excess dirt to leave the area in the
condition it was found. Make sure all
excess grease is removed and the datum point is clean.